neumann_dg.cc

The Helmholtz problem with Neumann boundary conditions by the discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "sinusprod_helmholtz.h"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
space Xh (omega, argv[2]);
size_t d = omega.dimension();
size_t k = Xh.degree();
Float beta = (k+1)*(k+d)/Float(d);
trial u (Xh); test v (Xh);
form a = integrate (u*v + dot(grad_h(u),grad_h(v)))
+ integrate ("internal_sides",
beta*penalty()*jump(u)*jump(v)
- jump(u)*average(dot(grad_h(v),normal()))
- jump(v)*average(dot(grad_h(u),normal())));
field lh = integrate (f(d)*v) + integrate ("boundary", g(d)*v);
field uh(Xh);
problem p (a);
p.solve (lh, uh);
dout << uh;
}
g
u_exact g
Definition: burgers_diffusion_exact.h:33
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
Float
see the Float page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
problem
see the problem page for the full documentation
rheolef::Float
double Float
see the Float page for the full documentation
Definition: Float.h:143
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
mkgeo_ball.f
int f
Definition: mkgeo_ball.sh:221
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:949
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::penalty
details::field_expr_v2_nonlinear_terminal_function< details::penalty_pseudo_function< Float > > penalty()
penalty(): see the expression page for the full documentation
Definition: field_expr_terminal.h:626
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition: field_expr_terminal.h:439
rk::beta
Float beta[][pmax+1]
Definition: runge_kutta_semiimplicit.icc:60
main
int main(int argc, char **argv)
Definition: neumann_dg.cc:29
rheolef.h
rheolef - reference manual
sinusprod_helmholtz.h
The sinus product function – right-hand-side and boundary condition for the Helmholtz problem.
a
Definition: diffusion_isotropic.h:25
p
Definition: sphere.icc:25
u
Definition: leveque.h:25
u
Float u(const point &x)
Definition: transmission_error.cc:26